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Showing papers in "Journal of Computational Physics in 1979"


Journal ArticleDOI
TL;DR: In this article, a second-order extension of the Lagrangean method is proposed to integrate the equations of ideal compressible flow, which is based on the integral conservation laws and is dissipative, so that it can be used across shocks.

6,630 citations


Journal ArticleDOI
TL;DR: In this paper, the critical flux limiting stage is implemented in multidimensions without resort to time splitting, which allows the use of flux-corrected transport (FCT) techniques in multi-dimensional fluid problems for which time splitting would produce unacceptable numerical results.

2,454 citations


Journal ArticleDOI
TL;DR: In this paper, a large number of different methods for numerically inverting the Laplace transform are tested and evaluated according to the criteria of applicability to actual inversion problems, applicability of various types of functions, numerical accuracy, computational efficiency, and ease of programming and implementation.

606 citations


Journal ArticleDOI
TL;DR: In this article, a review of recent work and new developments for the penalty function/finite element formulation of incompressible viscous flows is presented, in the context of the steady and unsteady Navier-Stokes equations.

548 citations


Journal ArticleDOI
Katuhiko Goda1
TL;DR: In this article, a numerical algorithm for solving two- or three-dimensional incompressible viscous Navier-Stokes equations is presented, which is based on a simple variant of the Chorin method and is related to the MAC method.

375 citations


Journal ArticleDOI
TL;DR: In this paper, a nonlinear hyperbolic system with an outflow boundary at chi=0 is considered, and the boundary condition at chi = 0 has been introduced only in order to limit the size of a computational problem.

328 citations


Journal ArticleDOI
TL;DR: Elliptic partial differential equations are used to generate a smooth grid that permits a one-to-one mapping in such a way that mesh lines of the same family do not cross.

274 citations


Journal ArticleDOI
TL;DR: In this article, a Chebyshev expansion technique was applied to Poisson's equation on a square with homogeneous Dirichlet boundary conditions, and the spectral equations were solved in two ways - by alternating direction and by matrix diagonalization methods.

257 citations


Journal ArticleDOI
TL;DR: The method provides an alternative to the conventional procedure which requires the numerical solution of a set of implicit nonlinear equations for the Lagrange multipliers by seeking a minimum of a concave function, a procedure which readily lends itself to computational work.

246 citations


Journal ArticleDOI
TL;DR: A finite element of the penalization type for the solution of incompressible viscous Navier-Stokes equations using an isoparametric parabolic element is presented in this article.

166 citations



Journal ArticleDOI
TL;DR: In this paper, an improved method of generating vectors for Monte Carlo integration is presented, which produces a significant improvement in rate of convergence over previous methods for problems in more than eight dimensions.

Journal ArticleDOI
TL;DR: In this article, the convergence properties of various finite-difference schemes for solving the equations of motion for recirculating flow of an incompressible fluid in a square 2D cavity are examined at Reynolds numbers up to 10'.

Journal ArticleDOI
TL;DR: In this paper, an initial value method based on the use of certain compound matrices was presented for the treatment of eigenvalue problems for stiff ordinary differential equations, which appeared to overcome not only the parasitic growth problems associated with standard shooting methods but also the difficulties, due to the presence of singularities, of the Riccati method.

Journal ArticleDOI
TL;DR: In this article, numerical schemes for the determination of stationary axisymmetric toroidal equilibria appropriate for modeling real experimental devices are given, where the toroidal current distribution is given by specifying the pressure and either the poloidal current or the safety factor profiles as functions of psi.

Journal ArticleDOI
TL;DR: In this article, the application of a dissipative Galerkin scheme to the numerical solution of the Korteweg de Vries (KdV) and Regularised Long Wave (RLW) equations is investigated.

Journal ArticleDOI
TL;DR: In this paper, nonlinear integral equations for the boundary functions which determine conformal transformations in two dimensions are developed and analyzed for numerical computations of conformal maps including those which deal with regions having highly distorted boundaries.

Journal ArticleDOI
TL;DR: In this paper, a multidimensional method of coordinate generation has been developed to match boundaries with coordinate surfaces and to control the manner in which other coordinate surfaces leave the boundaries, which is referred to as a multi-surface method.

Journal ArticleDOI
TL;DR: In this paper, a Lagrangian treatment of incompressible hydrodynamics with free surfaces is developed and applied to nonlinear free-surface waves and unstable shear flow beneath a free surface in two dimensions.

Journal ArticleDOI
TL;DR: In this paper, two scaling transformations are discussed which make possible such computations by reducing the computation time to acceptable levels and are shown to be valid for low-Mach-number flows.

Journal ArticleDOI
TL;DR: In this article, methods for the computation of sensitivity coefficients for constant, spatially varying, and temporally varying parameters in parabolic partial differential equations characteristic of reaction and diffusion processes are developed.

Journal ArticleDOI
TL;DR: In this paper, the Navier-Stokes equations for the steady motion of an incompressible fluid in 3D space were solved using a finite-difference scheme with second-order accuracy in which the associated matrices are diagonally dominant.

Journal ArticleDOI
TL;DR: In this paper, a numerical method is used to calculate the time evolution of the vortex sheet by adapting the ''Cloud In Cell'' technique introduced in solving many particle simulations in plasma physics, and two cases are considered for the initial distribution of circulation, one corresponding to an elliptically loaded wing and the other simulating the wing with a flap deployed.

Journal ArticleDOI
TL;DR: The use of piecewise quadratic polynomial approximations in the boundary integral equation method for the solution of boundary value problems involving Laplace's equation and certain Poisson equations is described in this paper.

Journal ArticleDOI
TL;DR: It is shown that interlaced meshes or mesh and submeshes may be employed to gain further computational economy and the algorithm and performance of a three dimensional implementation of the transform algorithm is given.

Journal ArticleDOI
TL;DR: The tensor viscosity method as mentioned in this paper is a generalization to two or three dimensions of interpolated donor cell differencing in one dimension, and is designed to achieve numerical stability with minimal numerical damping.

Journal ArticleDOI
TL;DR: In this paper, the authors investigate the numerical behavior of a set of difference equations and derive conditions under which solutions appear to be well behaved, and offer a physical interpretation of their behavior.

Journal ArticleDOI
TL;DR: In this article, two classes of boundary approximations are studied for viscous flow in a square cavity and compared with the results obtained by different methods of approximating the boundary values of the vorticity.

Journal ArticleDOI
TL;DR: In this paper, the numerical solution of a nonlinear hyperbolic equation not fulfilling the strict nonlinearity condition is considered, and a solution procedure is developed based on the random choice method, which permits the sharp tracking of discontinuities.

Journal ArticleDOI
TL;DR: In this paper, a Lagrangian type of MHD code was developed by treating elements of the fluid as finite-sized particles, i.e., position, mass, momentum and temperature, while the magnetic fields are advanced in an Eulerian manner.